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Theorem combi 485
Description: Commutation theorem for Sasaki implication.
Assertion
Ref Expression
combi a C (a == b)
Proof of Theorem combi
StepHypRef Expression
1 comanr1 464 . . 3 a C (a ^ b)
2 comanr1 464 . . . 4 a' C (a' ^ b')
32comcom6 459 . . 3 a C (a' ^ b')
41, 3com2or 483 . 2 a C ((a ^ b) v (a' ^ b'))
5 dfb 94 . . 3 (a == b) = ((a ^ b) v (a' ^ b'))
65ax-r1 35 . 2 ((a ^ b) v (a' ^ b')) = (a == b)
74, 6cbtr 182 1 a C (a == b)
Colors of variables: term
Syntax hints:   C wc 3  'wn 4   == tb 5   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  ublemc1  728
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